In flat bed knitting machines with a fine needle gauge, the comb gap between the needle beds can be so narrow that, in knitting take-off devices of the type mentioned above, the hook-shaped gripping elements must be made very thin and small in order to permit the elements to be guided through the comb gap. As a result, the gripping elements become unstable and can be bent in an undesirable manner well out of their adjustment plane by the tension exerted by knitting threads which have been grasped thereby. Moreover, there is a risk that no threads at all of the knitting edge will be grasped by the small hooks of many take-off hooks of a take-off hook strip.